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By G. Venturello, C. Antonione, G. Della Gatta

Results from work on the effect of inferstitials on recovery and recrystallization of' very pure iron (99.995 pet) doped with nilrogen up to 400 ppm are reported. Nitrided specimens were obtained by heating the iron in a static atmosphere of NH3 + H2. The samples were cold-rolled 80 pet, subjected to a series of isochronal and isothermal anneals, and submitted to examination by X-rays, micrographs, and hardness tests. Small additions of nitrogen show a strong effect in reducing recovery of' the mechanical properties of high-purity iron. At the temperatures of. the experiments, this effect proved greater than in the case of carbon. At 400°C pure iron recovers more than 50 pet of the total hardness increase, carburized iron vecovers 25 pet, and nitrided iron only 10 pet. On the other hand. the addition of nitrogen has, similarly to carbon, a very small effect on recrystallization; the effect is, however, slightly higher than that of carbon. When the concentration Of nitrogen is above the solubility limit in a iron at the temperattue of the experiments, an increase in the frequency of nu -cleation is also observed. THE object of the present work is to improve knowledge on the effect of interstitials both on recovery and on primary recrystallization of pure iron. In fact. at present there are no available data on the effect of nitrogen on high-purity iron. The only work which at present can be somewhat related to this problem is a work of Leak et al.1 in which grain boundary internal friction at high temperature in the presence of increasing amounts of nitrogen is studied by a torsion pendulum. The present work is a continuation of a previous one2 on the effects of carbon. EXPERIMENTAL PART Preparation of the Material. Pure iron was prepared following the same methods used in the pre- vious work2 and was nitrided using controlled quantities of ammonia in an apparatus similar to that used for carburizing. The apparatus consists essentially of a gas-tight quartz tube containing the specimens. The tube, maintained at constant pressure by means of a mercury seal, is placed in a resistance furnace. For nitriding, the NH3 + H2 atmosphere with a suitable concentration of NH3 was introduced into the tube, which had been previously carefully evacuated and degassed by heating at 600°C. The hydrogen used was carefully purified by passing it through a palladium filter. The ammonia required was prepared with the following reaction: CaO + 2NH4CI —CaCl2 + H2O + 2NH3 by heating the mixture of CaO and NH4C1 in a glass flask and then collecting the ammonia in a graduated Hempel burette. For each nitriding program a given amount of NH3 prepared by this method was introduced together with the H2 into the tube previously evacuated. Nitriding of the sample was then performed at 570°C for 48 hr. After this, to ensure a homogeneous distribution of nitrogen, the samples were further heated for 72 hr at 800°C. With this method which uses a static nitriding atmosphere, carefully controlled conditions of purity are obtained. Contrarily, with the conventional continuous-flow methods, using large quantities of circulating gas, there is a greater risk of introducing impurities into the samples. Furthermore, the required nitrogen concentration in the specimen is easily predetermined and obtained. A plot of the relation observed between the initial concentration of NH3 in the gas and the quantity of nitrogen introduced into the iron samples is given in Fig. 1. The data refer to samples of 1.2-mm thickness and to the nitriding conditions previously described. Furthermore, as a comparison, the data relative to two 0.5-mm-thick samples are reported. The presence of a reservoir in the cold zone of the reaction bulb made possible the gradual dissociation of ammonia on the sample in the hot zone. Internal-friction methods were used to determine the content of nitrogen dissolved in the iron samples. Some analyses were also carried out with chemical methods. The following table, Table I, shows a comparison of data obtained with chemical and internal-friction methods. The correspondence between chemical methods and internal-friction

Jan 1, 1964

By T. H. Alden

BaCKOFEN, Avery, and Turner have shown"2 that the large tensile elongation in superplastic metals is correlated with a high strain-rate sensitivity of the flow stress. At present, the reported superplastic materials are complex eutectic or eutectoid systems with a large solubility range in at least one of the terminal phases. This note describes the behavior of a solid-solution alloy (at 22°C)5,= Sn-1 wt pct Bi, which has been processed in order to produce a fine grain size.2,3,6 The chill-cast, 1/2-in.-diam ingot was homogenized for 1 week at 130°C, extruded at O°C to 0.083 in. diam, quenched within 15 sec, and stored at -196°C. Samples were warmed to room temperature 16 hr prior to mechanical testing or metallography. During tension testing at room temperature, it was found that the flow stress reached a steady-state value which depended on the imposed elongation rate and was independent of strain to an error of about ±5 pct. In Fig. 1 is plotted log a vs log e where a is the measured steady-state flow stress and i the imposed strain rate. These quantities were calculated using "instantaneous" area and length to an accuracy in the sample diameter of ±5 x 10-4 in. The log a-log 1 curve is sigmoidal. The strain-rate sensitivity, which may be given by d log old log 6,' has a maximum value of about 0.48 between i = 5 x 10-4 and 5 x 10-3 per min. The value is well above frequently measured values for metals at creep temperatures (0.1 to 0.3) and comparable to the rate sensitivity for Pb-Sn solder: which has been shown to be superplastic.2,3 Note, however, that below or above the strain rate of 10-3 per min the rate sensitivity of Sn-1 pct Bi decreases and at high rates is more nearly like that of conventional metals. The grain size of this material is relatively uniform, Fig. 2, and may be specified by an average linear intercept i.' Grain growth occurs at room temperature but after 16 hr, L = 5. Tensile elongation was measured on finer-grain-size specimens, which had been at room temperature 15 min prior to testing. After 15 min, the samples are fully recrystallized. Three strain rates, 5 x 10-3, 10-2, and 2.5 x 10-2 per min, were employed for which the measured elongations varied from 425 to 500 pct. These results would seem to justify the term superplastic, applied to this alloy, although the ductility is inferior to that of the Sn-Bi eutectic.3 The Sn-1 pct Bi alloy, which is a single-phase material with equiaxed, fine grains, is an excellent one on which to make an estimate of the Nabarro-Herring9 creep rate. According to the model of Avery and Backofen2 a substantial part of the deformation must be accomplished by N-H creep in the strain rate-temperature regime in which d log a/d log 1 = 0.5. The maximum N-H creep rate is given by9 L2kT where v is the atomic volume and D the self-diffusion coefficient. For this test v = 3.O x 10-23 cu cm, D = 1.4 e-23,300/RT = 2.5 x 10-l7 sq cm per sec,7 L = 5x 10+4 cm, T = 295°K, and a = 2000 lb per sq in. = 1.38 x 10' dyne per sq cm. The calculated creep rate is E= 4 x 10-11 per sec which may be compared with the measured creep rate at this stress, Fig. 1, of 6.7 x 10-5 per sec. The N-H creep rate is seen to be negligible. Earlier consideration2 of this question was in error because incorrect diffusion coefficients were used. The assistance of R. R. Russell in metallography is acknowledged gratefully.

Jan 1, 1967

By R. E. Pray, M. C. Fuerstenau, J. D. Miller, B. F. Perinne

Quartz cannot be floated with potassium amyl xanthate as collector at any pH. Complete flotation is achieved with certain minimal additions of amyl xanthate and Pb from pH 5.8 to 8.5 and with amyl xanthate and Zn from pH 7.5 to 8.1. The active species of these metal ions responsible for activation are shown to be PbOH and ZnOH No flotation was effected when Cu and Mg were added as activators. Previous work1,2,3,4,5,6,7 has shown that quartz may be floated in the presence of sulfonate or soap when the following two criteria are met: 1) some portion of the added metal ion has hydro-lyzed to its first hydroxy complex, and 2) a precipitate of the metal-collector has formed. Since sulfonate and soap, two substantially different anionic collectors, conform to these criteria, this phenomenon may well be expected to be of a general nature. In this view then, it would appear that any anionic collector, including xanthates, should also float quartz when these two criteria are met. The object of this paper is to demonstrate the conditions under which quartz will respond to flotation in the presence of potassium amyl xanthate. EXPERIMENTAL MATERIALS AND TECHNIQUES Quartz was prepared by leaching the sized sample (48 x 150 mesh) with HC1 until no iron could be detected in the leach liquor. Conductivity water, made by passing distilled water through an ion exchange column, was used in the investigation. Potassium amyl xanthate was selected as collector. Purification of this reagent was effected with the following method: 1) a laboratory sample of potassium amyl xanthate was dissolved to saturation in hot ethyl alcohol and filtered several times while still hot, 2) the filtrate was cooled, during which time potassium amyl xanthate crystallized out of solution; the xanthate was then separated from the solution by filtration, 3) the amyl xanthate was dissolved in fresh hot ethyl alcohol and filtered, 4) step (2) was repeated, 5) the crystalline potassium amyl xanthate was washed with ethyl ether five times, and 6) the xanthate was dried for 24 hours under continuous vacuum. Inorganic impurities are insoluble in hot ethyl alcohol whereas dixanthogen is soluble in ethyl ether. Five-gram charges of 48x150 mesh quartz were conditioned for 3 min in 125 cc of solution containing the reagents and were floated with the small-scale cell and procedure described in previous papers.478 Reagent grade HCl and NaOH were used for pH adjustment, while reagent n-amyl alcohol was added as frother. Frother addition is necessary with this technique, but it should be mentioned that data, similar to those shown in Fig. 2 for 1 x10-4 mole per liter Pb++ and 1 X 10-4 mole per liter AX-, were also obtained with a Hallimond cell in the absence of frother. EXPERIMENTAL RESULTS Clean quartz could not be floated with amyl xanthate at any pH. Flotation was achieved under certain conditions, however, when various metal ions were added to the system. The activating ions used were lead, zinc, copper and magnesium, added as reagent grade chloride salts. Lead as Activator: The effect of Pb++ as activator was examined at five different additions of amyl xanthate (Fig. 1, 2 and 3). When 1x 10-5 mole per liter xanthate was added in the presence of 1 x 10"4 mole per liter Pb ++, no flotation was obtained at pH 6.5 or below, while a recovery of about 60% was effected at pH 7. When the pH was increased to 7.8, no flotation was again obtained, Complete depression was noted from pH 7.8 to about 10, at which point a recovery of about 30% was achieved. At about pH 11, the precipitate of lead amyl xanthate which was present below this pH dissolved and complete depression occurred. When 2.5x 10-5 mole per liter xanthate was added with the same lead addition, no flotation was obtained at pH 5.8 and below, whereas a recovery of

Jan 1, 1965

By V. Koump, T. F. Perzak, R. G. Olsson

The rate of dissolution of recrystallized alumina in molten iron oxide in equilibrium with iron at 1450°C was studied by rotating alumina disks in the melt. The samples were rotated from 1 to 12 min at speeds from 54 to 3270 rpm. It is concluded from the experimental results that the process is limited by diffusion in the liquid boundary layer. The interdiffusion coefficient for the dissolution of alumina disks in pure molten iron oxide was estimated to be about 3 xl0-5= sq cm per sec. THE erosion of refractory materials is of considerable importance in iron- and steelmaking processes. Since many refractories contain alumina, this investigation was undertaken to develop a further understanding of the erosion mechanism. Shurygin et al.1-3 have investigated the rate of dissolution of alumina in molten silicates and molten fluorides by rotating alumina disks in various melts. The rates were reported to be limited by diffusion in the liquid boundary layer. In the present investigation the rate of dissolution of alumina in molten iron oxide in equilibrium with iron was studied in a similar manner; alumina disks were rotated at different speeds in molten iron oxide at 1450°C. The relationship between the rate of dissolution of the flat surface of the disk and the speed of rotation was used to determine whether the process is limited by diffusion in the liquid boundary layer or by some chemical reaction mechanism. APPARATUS AND EXPERIMENTAL PROCEDURE A schematic diagram of the experimental apparatus is shown in Fig. 1. The iron oxide melts were contained in 2-in.-diam high-purity iron crucibles that were centered in a cylindrical graphite susceptor. Prior to each sequence of experiments, sufficient reagent-grade ferric oxide was added to a crucible to form approximately 350 g of molten iron oxide; the depth of the melt was about 11/2 in. To prevent excessive erosion of the crucible, about 70 pct of the required iron was added to the crucible in the form of iron powder. The mixture was melted in an atmosphere of purified argon by induction heating with a 250-kc generator. After the oxide was molten, a Pt/Pt-10 pct Rh thermocouple at the exterior of the crucible was calibrated against an iron-sheathed thermocouple immersed in the melt and was thereafter used to regulate the melt temperature. All experiments were conducted at 1450°C with a probable error of 10°C. The alumina disks were constructed from pure re-crystallized alumina having a density of 3.7 g per cu cm (porosity approximately 6 pct). For each disk sample a 1-cm-diam alumina cylinder of known length (0.9 to 1.0 cm) was cemented into a ground seat at the end of a 1.27-cm-OD centerless ground alumina tube. The ends of the tube and cylinder were flush and served as the disk surface. When mounted in the apparatus the alumina tube was guided by tungsten carbide bearings and rotated by a variable-speed motor. The bearing and drive assembly could be raised and lowered in order to allow the sample to be quickly moved in and out of the melt. At the start of an experiment, a sample was preheated for several minutes directly above the melt, and then immersed in the middle of the melt to a depth of a in. and rotated for 1 to 12 min at speeds of 64 to 3270 rpm. The speed of rotation was measured by a hand tachometer. At the start and completion of each experiment, a melt sample was withdrawn with a cold copper rod and the alumina content was determined by chemical analysis. During individual experiments the alumina concentration of the melt changed by the order of 0.25 wt pct. Average melt compositions for individual experiments were used in the subsequent computations and were in the range between 0.12 and 4.3 wt pct alumina. The extent of dissolution was determined by sectioning the end of the sample and measuring the final length of the alumina cylinder with a microscope. Since the exposed end of the cylinder, i.e., the disk surface, was etched in a manner characteristic of this geometry, a number of measurements were made on

Jan 1, 1969

By C. W. Allen, B. D. Cullity

The proportional limit of iron crystals in torsion is governed by the resolved shear stress in the most highly stressed slip systems, averaged around the specimen circumference, and does not obey a critical resolved shear stress law. Crystals of most orientations exhibit a stage of easy plastic deformation, akin to easy glide in tensile or shear specimens. Transient deformation, similar to that which occurs in single crystals of other materials, is also observed. THE torsional deformation of single crystals of magnesium (hcp) and aluminum (fcc) has been described recently by Choi et al.,&apos; especially with respect to the criterion for the orientation dependence of the onset of plastic flow in these materials. The purpose of this paper is to present results of torsion tests of iron single crystals and thus to extend this yield criterion to a bcc metal. In addition to considering the variation of proportional limit with crystal orientation, this paper also briefly treats work hardening, transient deformation, and the mechanism of plastic flow in iron. The effects of the method of surface polishing and the chemical purity of the iron have been investigated. STRESS DISTRIBUTION It is convenient to express the stress at any point of a cylindrical crystal stressed in torsion in terms of t0, which is the shear stress acting at the surface on a plane normal to the axis of the cylinder and in a direction tangential to the cylinder. This stress is given by To = 2T/pr3 [1] where T is the applied torque and r the specimen radius. The shear stress t, resolved in any chosen slip system is given in terms of 7, by1 Ts/TO = sin 0, cos d sin (0, -) + cos , sin d sin d - ) [2] where 0 and d are the angles between the specimen axis and the slip plane normal and slip direction, respectively; h is the angular circumferential position on the specimen at which t, is being determined, measured from an arbitrary reference plane which includes the axis;o and d are the angular coordinates of the projections of the slip plane normal and slip direction on a transverse section with respect to this same reference plane. Slip in iron occurs in a <1ll> direction on the {ll0}, (1121, and (123) planes, which together comprise 48 slip systems. A complete evaluation of the stress distribution in an iron crystal stressed in torsion would therefore require a calculation of Ts/T0 as a function of for 48 different slip systems. Fortunately Gough,&apos;who studied the behavior of iron crystals in alternating torsion, was able to simplify this problem considerably. He showed that it was sufficient to consider a kind of average slip plane for each slip direction, namely the mathematical plane of maximum resolved shear stress containing the slip direction considered. This simplifying approximation is possible because, for each slip direction, the active slip plane or planes lie very near this mathematical plane of maximum shear stress. Vogel and rick&apos; have critically reviewed the early work of Taylor and Elam,13 Taylor,14 and Fahrenhorst and schmid8 from which the identification of the above crystallographic planes as slip planes in the bcc lattice largely stems. While their criticism is clearly justified, their own results do little to clarify the issue. The role of cross slip (screw dislocations changing glide planes) is evidently so important in this case, as Read3 has suggested, that methods for deducing slip systems from observations of gross slip traces are inadequate, such traces commonly arising from complex dislocation motion. Thus the treatment given here involving the plane of maximum resolved shear stress seems a logical simplification especially in view of Gough&apos;s2 study of a iron. There is, however, an assumption built into the subsequent treatment the comparative validity of which is difficult to assess, namely, that slip in all slip systems in iron may be characterized by a common critical resolved shear stress. The shear stress 7, resolved in a slip direction defined by d andd, and on the plane of maximum shear stress containing this direction, is found by first maximizing 7s/70 with respect to either Oo or 4,. The slip plane coordinates are then eliminated by using the relation between 0, ,o and d, d, namely,

Jan 1, 1963

By M. R. Tek, K. H. Coats, D. L. Katz

The nature and the limits of validity of Darcy&apos;s law US applied to the flow of natural gas through reservoirs has been considered in order to resolve some controversial aspects of the effect of turbulence on pressure drops. The equivalence between various concepts and viewpoints advanced in the past by several investigators to explain how and why a gas well does not necessarily perform according to Darcy&apos;s law is shown. Starting with generalized equations of flow of fluids through porous media, a partial differential equation has been derived which accurately represents the flow at all rates. This equation has been numerically solved using an IBM 704 digital computer. The results permit plots of unsteady radial pressure distribution curves from which specific isochronal backpressure curves may be constructed. These back-pressure curves show the effect of the ,8 factor on the slope of the back-pressure curve. The calculations further indicate that the drainage radius for a gas well in turbulent flow propagates at a rate dependent upon the rate of production at the wellbore. This is quite different from the case with liquid flow or natural-gas flow in laminar regime. Additionally, the effect of reservoir inhomogeneities and crossflow between layers of different permeability on the back-pressure performance of gas wells has been conridered. In light of the current numerical results the significance and linlitation of the rate of flow function Y proposed by Smith" has been discussed. INTRODUCTION The relationship between the pressure drop and flow rate in problems of fluid flow through porous media is known to be affected by the nature of flow through the porous matrix. It has been observed by many that, for a range of flow rates, the pressure drop remains proportional to the rate of flow. When some flow rate is reached, however, it is usually observed that the pressure drop gradually begins to increase more than proportionally to the flow rate. It is well known that this phenomenon was first observed by Osborne Reynolds in 1901 in experimenting with flow through pipes. In his classical experiments, Reynolds made visual observations on the condition of streamlines evidenced by injecting a dye into water flowing through glass tubes. In these experiments, the abrupt transition between steady, "streamline, laminar" flow and unsteady random turbulent flow was found to be a function of the dimensionless group (Dvp/u), now known as the Reynolds number. During these experiments, in addition to observations on the nature of flow regimes, the proportionality between flow rate and pressure drop in laminar flow was contrasted with the nonlinearity between these variables in turbulent flow. Fancher and Lewis&apos; reported data on various consolidated and unconsolidated sands in 1933. Their conclusions were that ". . . the flow of fluids through these porous materials closely resembles that through pipes; that there is a condition of flow in porous systems which resembles viscous flow, another which corresponds to turbulent; that the change from one type to the other takes place at a definite and reproducible condition for each system". In 1947, Brownell and Katz published a method to predict the laminar and turbulent flow behavior from the particle size, bed porosity and the particle sphericity, employing the friction factor-Reynolds number charts for pipes. Several investigators have verified the work of Fancher, Lewis and Barnes and presented their data as friction factor-vs-Reynolds number plots.&apos; The equation which would represent the pressure gradient over the whole range of velocity must have an added term over that represented by Darcy&apos;s law. Accordingly, the pressure gradient necessary to sustain flow at the velocity (v) through a porous medium may be represented by the following equation, suggested by Forscheimer." The nature and the range of validity of Darcy&apos;s law has been the subject of studies by many investigators over the past years. While everyone seemed to agree on the need for a quadratic correction term to Darcy&apos;s law to make it effective over the range of velocities, the concept of inception of turbulence and the use of the term "turbulent flow" remained controversial. Some fluid dynamicists define turbulence as a flow

By Elmer Weber, W. M. Baldwin

Solid lead obeys a single parabolic weight increase vs. time law. In contrast, liquid lead undergoes three successive parabolic weight increases vs. time laws, the first of which has a low constant relative to the latter two. The conversion times for the change from one parabola to the next decrease with increasing temperature. IN recent reports on the subject,1,2 it was noted that zirconium and titanium scale in air by a complex mechanism. The scale first forming on the metal is protective to the extent that it gives a low constant, K, for Tammann&apos;s, and Pilling and Bedworth&apos;s parabolic equation: w² = Kt [1] relating weight increase, w, due to chemical reaction of the metal with the air, and time, t. After hundreds of hours of apparent stability in some cases the first scale yields to another that offers little protection to the metal. This transition from one scale to another, from a slow parabolic oxidation reaction to a fast one, was not due to impurities in the atmosphere or incidental effects (changing environment, etc.) but was a specific behavior of the metal itself, the transition occurring at definite times (dependent on temperature) and showing other reproducible traits. In view of this behavior how can long-time service behavior be predicted from short-time laboratory tests, not only in the case of these metals, but in any case? Certainly a systematic study of the type of scaling behavior described above—wherever it is found—would help to answer this question. The present paper is a report on the behavior as it is found in lead—the only metal to the authors&apos; knowledge for which the behavior has been described at all, if inadequately, for our present purpose.* At least four oxides of lead are known, of which one occurs in two allotropic forms. They are ß (red) tetragonal PbO stable up to 486°C;8 a (yellow) orthorhombic PbO stable from 486°C up to its dissociation temperature in air at about 2300°C;9 minium or Pb3O4 which from the dissociation pressure data given in Fig. 1 decomposes to PbO at 540°C in air; lead sesquioxide or Pb2O3,; and lead dioxide or PbO2 which, according to Fig. 1, decomposes in air at 400°C to minium. In view of the high dissociation temperature of PbO, lead will scale up to at least its boiling point. Further, it is known that oxygen is almost insoluble in liquid lead.&apos;V his implies a fair probability that an oxide scale would not dissolve in the molten metal and would afford the same protection to lead in the liquid state as in the solid. All of the oxides of lead for which specific gravity data are available are more voluminous than an equivalent weight of metal or a lower oxide from which they might form, hence the scales will be in compression. Lead oxides are known to be ductile, so it would be anticipated that they would form coherent nonporous scales. It is not surprising to learn, then, that both solid and liquid lead scale according to the Tammann, and Pilling and Bed-worth law.14,15 (Gruhl states that at 600°C and above lead oxidizes linearly with time because of "spitting" of the scale.) The parabolic constants K reported by various investigators3,14-16 are badly scattered, however, as shown in Fig. 2. The oxides formed on solid lead were described as being reddish-brown but were not chemically identified by Pilling and Bedworth.15 Gruhl&apos;s descripdin³ of the appearance of the scales On his liquid samples indicates that a (yellow orthorhombic) PbO is formed initially on the specimens but gives Way eventually—at least at temperatures below 486 °C— to .ß (red tetraunal) PbO, and that below 540°C minium—Pb3O4 :is firmed at an even later time as an overlay on either the red or yellow PbO. Fig. 3 is a graphical interpretation of Gruhl&apos;s description. Gruhl does not indicate any change in the parabolic scaling rate as yellow PbO converts to red. He does indicate that minium reduces the scaling rate, al-

Jan 1, 1953

By O. R. Wagner, R. O. Leach, H. W. Wood, C. F. Harpke

PAN AMERICAN PETROLEUM CORP.TULSA, OKLA. CASPER, WYO A field test has been made in which additional oil recovery was obtained from a previously-waterflooded "oil-wet" sandstone reservoir. This recovery improvement was accomplished by adjusting the reservoir wettability through chemical treatment of the flood water. The test was made in the Muddy sand of the West Harrisburg Unit, Neb. The chemical used, sodium hydroxide, was injected as a slug of dilute caustic solution through a water-injection well. The natural wettability of the reservoir and the chemical requirements for reversing wettability were determined in the laboratory from contact-angle studies using field water and oil samples. Laboratory flood tests with a synthetic system had shown that reversing the wettability of an oil-wet consolidated core would lead to improved oil recovery. The field performance indicates that the mechanism by which increased oil retovery is obtained in the field is the same as that observed in the lahoratory. Laboratory studies indicate that higher ultimate recoveries and decreascd water-injection requirements result when the adjusting agent is added early in the life of the flood. However, a previously waterflooded area was intentiorzally chosen for the field test so that unambiguous conclusions could be made about the effects of chemical injection on wettability and the extent of oil-recovery improvernent afforded by wettability reversal. Forces existing at the fluid-solid and fluid-fluid interfaces in a porous medium have an important effect on oil recovery during a water flood. Modifying these interfacial forces in the reservoir to improve oil recovery has been the object of much research. Several papers&apos; &apos; have discussed the use of surfactants to lower the water-oil interfacial tension. This paper describes work concerned with improving oil recovery by modifying the forces at the fluid-solid interfaces— that is, by changing the preferential wettability. An earlier paper: presented evidence to show that some reservoir systems could be changed from preferentially oil-wet to preferentially water-wet by the action of simple chemicals added to the water to increase waterflood oil recovery. The process was attractive for further study because it used only inexpensive chemicals and because it called for a gross "wettability reversal" rather than for a precise adjustment. The present paper is an extension of the earlier work. Laboratory flow tests were made using treated water and oil in a consolidated core to determine the amount of additional oil recovery and the producing performance which might be expected from reversing the wettability of an oil-wet reservoir during a flood. A contact-anglc study using water and oil from the Muddy "J" sand of the Harrisburg field, Banner County, Neb., indicated the reservoir to be preferentially oil-wet and susceptible to wettability reversal through chemical injection. Based on these studies, a field trial of wettability-reversal water flooding was initiated. in the Harrisburg field. The primary purpose of the trial was to determine if wettability-reversal flooding would improve oil recovery in an actual field situation. The field trial was also an important test of the laboratory tecnique used to determine the effect on oil recovery of certain wettability manipulation, as well as a test of the contract-angle method of determining reservoir wetra-bility. The paper is presented in two parts. The first part covers the laboratory experiments leading up to the field trial, and the second part covers the field trial. PART I—LABORATORY STUDY The laboratory experiments consisted of displacement tests using an idealized fluid system and of a contact-angle study with crude and water from the Muddy "J" sand of the West Harrisburg Unit, Banner County, Neb. The displacement tests were designed to determine the effects of a particular wettability manipulation, oil-wet to water-wet, on oil displacement in a water flood. The contact-angle measurements were made to determine the natural wettability of the reservoir and to determine if beneficial wetting changes could be brought about by a chemical addition to the flood water. PROCEDURE DISPLACEMENT TESTS The displacement tests were perfornled in a consolidated sandstone core using a refined oil and water. The wetting properties of this system could

By R. Taggart, D. H. Polonis, W. C. Gallaugher

In the Ti-Cu system, the a&apos; phase can be produced over a wide range of alloy composition witJwut the retention of measurable amounts of the ß or ? phases. This paper reports on the decomposition of this hexagonal martensite phase front the standpoint of solute corzcentratiorz, tempering temperature, and coherency strain condition. The mechanism of precipitation during tempering comprises localized precipitation which is followed by discontinuous precipitation if sufficient coherency strains are present. The localized precipitation process in hypoeutectoid alloys is described by the generalized Johnson-hiehl equation and an activation energy of 46,000 cal per mole. In hypereutectoid alloys the corresponcEing activation energy is 51,000 cal per mole. The rate-controlling process has been proposed as the difision of copper along a&apos; platelet interfnces. SEVERAL investigations have been reported concerning the kinetics of decomposition of the mar-tensitic a&apos; phase in titanium binary alloys.&apos; In the Ti-Mo system,&apos; two modes of a&apos; decomposition have been observed in the presence of /3 phase; one of these involves the precipitation of fine a from a&apos;, and the other involves diffusion across the a&apos;-ß interface. In studies of the Ti-Cr system, Rostoker2 did not detect the formation of TiCr2 during tempering. In Ti-Ni alloys,3 the intermediate phase Ti2Ni has been found to precipitate directly from a&apos; along the interfaces between plates. With the exception of the study of Ti-Ni alloys the previous investigations of tempering phenomena in substitutional martensites are mainly qualitative and do not present a detailed description of the precipitation processes. The following limitations restrict the correlation of the microstruc-tural processes and reaction kinetics during tempering in most binary-alloy systems. 1) A mixture of at least two phases characterizes the constitution of quenched alloys. 2) Difficulties have been encountered in obtaining uniform structures throughout quenched samples. 3) The reaction products, and in particular their morphology. have not been clearly resolved. 4) The martensitic a&apos; phase forms over only a limited composition range for most titanium-base binary alloys. Gomez and polonis4 showed that the Ti-Cu system provides an excellent basis for investigating the tempering of a&apos; over a range of composition without the complication of retained P or the transition w phase. In the present work the effects of solute concentration, tempering temperature, and coherency strain conditions are considered with reference to the over-all precipitation process in quenched alloys of the Ti-Cu system. Both microstructural observations and kinetic data are correlated to define the rate-controlling processes which govern the observed localized and discontinuous precipitation reactions. An earlier paper5 was devoted to a discussion of the modes of heterogeneous nucleation of Ti2Cu from the martensitic a&apos; structure. The present paper will therefore emphasize the progress of the tempering reaction beyond the initial stages. EXPERIMENTAL METHODS The Ti-Cu alloys for this study were prepared by conventional arc-melting procedures. Chemical analysis revealed that the alloy buttons contained approximately 0.02 wt pct 0, 0.04 wt pct N, and within 0.1 wt pct of the intended copper concentration. The progress of the tempering reaction was followed by means of electrical-resistance measurements utilizing a Kelvin double bridge, microhard-ness readings with a 400-g load, and X-ray dif-fractometry patterns to reveal line-broadening effects. Metallographic specimens examined at magnifications greater than X1000 were shadowed with germanium to reveal fine structural details. Direct carbon replicas were prepared for the electron-microscopy studies. EXPERIMENTAL RESULTS Property Changes. The changes of microhardness that accompany the precipitation of Ti2Cu from a&apos; are shown in Figs. 1 and 2. As the solute concentration increases the peak hardness, for a given tempering temperature, increases. In alloys of given composition the time to reach the peak hardness agreed with the time to attain maximum X-ray diffraction peak breadth, as shown in Fig. 3. The maximum hardness and the maximum line breadth increased with lower tempering temperatures, and the time to reach the maximum also increased. The a&apos; peaks broadened during the initial stages of tem-

Jan 1, 1965

By W. O. Philbrook, R. S. Kaplan

Rates of oxidation were studied for levitation-melted samples of Fe-C, Fe-Si, Fe-C-Si, Fe-C-P, Fe-C-Mn, and Fe-C-S alloys oxidized by mixtures of either 5 or 10 pct O2, in helium at several temperatures in the range 1850o to 2050°C. The concentrations of the oxidized elements decreased linearly with time. Mass transport in the gas phase was found to be the rate-controlling step. Ilowever, a mulliple -film model was necessary to account for the flux of iron and manganese vapor counter to the oxygen flow. THE advent of the basic oxygen and spray-refining processes of steelmaking has generated considerable interest in the kinetics of reactions between oxygen-bearing gases and liquid iron alloys. The object of this research was the determination of the role of mass transport in the gas and metal phases and of surface chemical reactions in the overall oxidation process. Of the reactions for elimination of elements dissolved in liquid iron, the oxidation of carbon has been investigated most extensively. Studies by Fuji and Ura,1 Fuji,&apos; and Gunji et a1.,3 done with pilot-scale basic oxygen furnaces, indicated that mass transport of gaseous oxygen was rate controlling when the metal carbon content was greater than 0.15 to 0.30 pct. When the carbon content was less than this critical amount, diffusion of carbon dissolved in the iron was thought to be rate limiting. L. A. Baker et a1.4,5 levitated samples of iron-carbon alloys and oxidized them in CO-CO2, CO-C02-He, and O2-He atmospheres at 1660°C. These investigators found that the metal carbon concentration decreased linearly with time and their samples exploded when the carbon content fell below about 0.8 pct. They concluded that the rate-limiting step was the transfer of oxidant to the gas-metal interface. A model based on this rate-limiting step predicted decarburization rates within a factor of two of those experimentally observed. The explosion of the samples was attributed to a shift in rate-controlling step from gas-phase mass transport to transport of carbon dissolved in the metal. L. A. Baker and R. G. ward6 and R. Baker7 used freely falling droplets to investigate oxidation kinetics. In both papers, the authors speculated that flame fronts may have been partially responsible for the lack of better agreement between experiment and theory. Swisher and Turkdogan8 oxidized liquid iron having an initial carbon content of 0.97 pct with CO-CO2 and CO-C02-Ar mixtures at 1580°C. They concluded that a surface reaction was the rate controlling step. Iron-silicon alloys have been oxidized by R. Baker7 and Filipov and Martynov.9 R. Baker 7 also studied iron-carbon-silicon alloys falling as liquid droplets through oxygen. He found that the rate of both carbon and silicon oxidation varied inversely with the drop radius. When the initial silicon concentration was greater than 6 pct, the samples cooled during their fall. Manganese oxidation has been studied by R. Baker,7 and by Filipov and Martynov.9 ward10 investigated the loss of manganese from liquid iron under vacuum. He found that mass transport of manganese vapor was rate limiting in argon atmospheres of 0.02 torr to 700 torr pressure. Iron-sulfur alloys were desulfurized with H2-He and H2-Ar mixtures by Peters et al.11 A model based on the transport of H2S from the gas-metal interface into the bulk gas gave fair agreement between the predictions of the model and the experimental results. EXPERIMENTAL TECHNIQUE Essentially, the technique consisted of using helium-oxygen gas mixtures to oxidize levitated samples of liquid binary and ternary iron-base alloys. The fused silica reaction tube is shown in Fig. 1. The coil design is similar to that of L. A. Baker et al.4&apos;5 A Tef-lon-sheathed, ferritic stainless steel lifter (B) and an alumina pedestal (C) were used to support the sample in the coil prior to levitation and for the recovery of the sample. Samples were inserted into

Jan 1, 1970

By R. A. Breitrick, J. N. Swinderman, J. J. Cooper, H. L. Bauer Jr.

The Robinson Mining District, near Ely, Nev., is one of the major porphyry copper districts in the world. Within the district is an eight mile long east-trending zone of altered porphyry, metamorphosed sedimentary rocks, and sulphide mineralization surrounded by Paleozoic limestone, dolomite, shale and sandstone, Tertiary volcanics, and Quaternary alluvium. Six major disseminated ore deposits have been exploited in this zone. About 20% of the district production has come from disseminated ore in metamorphosed sedimentary rocks found adjacent to altered quartz-monzonite porphyry. The following brief statements summarize some of the relations between porphyry alteration, metamor-phism, and mineralization: 1) Disseminated copper ore does not occur in unaltered porphyry or in m-metamorphosed sedimentary rocks. 2) Sedimentary rocks have been only weakly metamorphosed where intruded by unaltered porphyry. 3) Intensely metamorphosed sedimentary rocks are found only adjacent to altered porphyry. 4) Many hydrothermal minerals are common to both altered porphyry and adjacent metamorphosed sediments. 5) Disseminated ore is found in altered porphyry and adjacent metamorphosed sedimentary rocks. 6) In general, there is a direct correlation between grade of ore in porphyry and copper content in the adjacent rocks. 7) Chemical changes in the altered porphyry and metamorphosed rocks appear to be related. The foregoing relations support a hypothesis that the porphyry alteration, the metamorphism of the sedimentary rocks, and the ore deposition were all part of a continuous hydrothermal process which probably closely attended the porphyry intrusion. The Robinson Mining District, most often referred to as the Ruth or Ely District, is located in eastern Nev. and is one of the major porphyry copper districts of the world. Production from 1908 through 1962 was nearly 250 million tons of ore averaging a little over one percent copper with a total metal value of nearly one billion dollars. The ore has been produced from six major disseminated-type deposits with the Liberty Pit deposit accounting for 70% of the total district production. Less than one million tons of base metal and gold ores have been produced from the replacement-type deposits of the district. Approximately 20% of the district production has come from underground mining operations; the pit ore has been mined with shovels and removed by train haulage, truck-train haulage combinations, truck haulage, and presently by a combination truck-skip system. Many of the ore deposits formerly worked by underground methods have been and are being exploited by open pit methods. (See Fig. I.) Two co.&apos;s have accounted for virtually the entire production from the district. In 1958 Kennecott Copper Corp. acquired the district assets of Consolidated Coppermines Corp. and is now the sole ore producer in the district. Present operations are confined to the Liberty Pit where 22,500 tons of ore averaging a little less than 0.8% copper is mined per day. Cutoff grade is 0.4% copper, and the stripping ratio is three to one. The ore is hauled by rail 23 miles to the McGill Reduction Plant where it is concentrated to about 20% copper. Molybdenite is recovered as a by-product in the mill. The copper concentrates are smelted in McGill, and the blister copper is shipped for refining to Balt. where gold, silver, platinum and palladium are recovered. The Robinson Mining District has been well known as a porphyry copper district for the past fifty years, but many geologists are unaware of the fact that a large portion of the production has come from disseminated ore found in metamorphosed sedimentary rocks. The scope of this paper describes the occurrences of disseminated ore in the various metamorphosed sedimentary rocks, and presents evidence for the hypothesis that these ores are genetically, spacially, and coevally related to the disseminated ore in the porphyry rocks. Publication of this paper was granted by the management of Kennecott Copper Corp. A. H. James suggested and encouraged the writing of the manuscript. Special mineralogical and spectrographic analyses were performed by the Kennecott Research Center. The deposits of the district have been studied by many geologists since the turn of the century, and

Jan 1, 1964

By E. R. Buchanan, R. E. Reed-Hill

Cylindrical magnesium single crystals were deformed in torsion. The axis of torsion was the basal pole. Five crystals were deformed to different strains between 0.08 and 1.03 and then sectioned in order to determine their dislocation densities using the transmission electron microscope. The work hardening rate of all specimens was at least an order of magnitude higher than that normally associated with easy glide in a tension test and comparable to that obserzed in stage B of a tension test. The correspondence between stage B in a tension test and the initial stages of a torsion test is believed to result from the fact that in both cases deformation occurs in a structure containing roughly equivalent densities of the dislocations associated with the three basal slip vectors. THERE are three basic ways of changing the shape of a crystal using slip dislocations. The crystal can be sheared along a slip direction in a slip plane; it can be bent about an axis in the slip plane normal to the slip direction; and, if the slip plane contains multiple slip directions, it can be twisted or rotated about the slip plane normal. Of the three processes, generally known as translational, flexural, and rotational slip, only rotational slip has not been extensively investigated. The object of the present research was to obtain basic information about this phase of crystalline plasticity. This paper is concerned with some aspects of the stress-strain curves obtained by twisting magnesium crystals about their basal poles. Magnesium was selected for four reasons. One, its recovery rate at room temperature is relatively low. Two, single crystals may be easily grown. Three, at room temperature the critical resolved shear stress for basal slip is about two orders of magnitude lower than that for nonbasal slip, so that rotational slip might be expected to occur primarily by basal slip. Finally, relationships between flow stress, shear strain, and dislocation density have been determined for tensile deformation of magnesium crystals,&apos; thereby providing a basis of comparison for the torsional results. EXPERIMENTAL PROCEDURES Crystals were grown from 0.5 in. diam extruded sublimed magnesium rod furnished by the Dow Chemical Co. who reported that it contained in weight percent less than 0.0003 Al, 0.01 Ca, 0.01 Cu, 0.0012 Fe, 0.001 Mn, 0.0005 Ni, 0.003 Pb, 0.001 Si, 0.01 Sn, and 0.02 Zn, with the balance magnesium. All crystals were grown in a dried argon atmosphere using Jill-son&apos;s2 modified Bridgman technique. Two different methods were used to obtain crystals with the basal plane normal to the specimen axis. These included direct growth from seeds of the proper orientation, and spark machining (trepanning) of 0.5 in. diam cylinders from larger (1.5 in. diam) randomly grown crystals. The crystals thus produced were polished in a 20 pct HC1 water solution and then etched in a 1 pct HC1 water solution to develop etch pits lying in rows parallel to the basal plane trace. The crystals were then revolved about their axes on the stage of a low-powered microscope. Torsion specimens were prepared only from those crystals whose axes were normal to the rows of etch pits. It is estimated that this simple orientation method was accurate to about 51 deg. 1.625 in. long cylinders were next cut from these selected crystals and then acid machined in a 20 pct HC1 water solution into torsion specimens with a 1 in. long by 0.30 in. diam reduced gage section. Following this, they were annealed in air at 400°C and furnace cooled to room temperature. The specimens were given a final polish in a 10 pct HC1 water solution, rinsed in ethanol, dried, and cemented into brass grips with an epoxy resin. In addition to the torsion specimens, several tensile specimens with their basal planes at 45 deg to the stress axis were also prepared with similar dimensions except that the gage sections were increased to 4 in. in length. The torsion specimens were tested in the apparatus

Jan 1, 1970

By A. W. Sommer, H. H. Kellogg

It is shown that SO3-O2 mixtures react with sphalerite at an appreciable rate ill the temperature range of 361° to 527°C to fornz ZnSO4. The rate of reaction follows a parabolle lax. Oxygen, or O2-SO2 mixtures, have a negligible effect on sphalcrite in the same temperatuee range. PRACTICAL roasting of sphalerite is usually performed at 800°C or higher. The calcine is composed of zinc oxide unless the roaster atmosphere contains relatively large amounts of SO2 and the temperature is held to 800oC or lower, in which case zinc sul-fate may also form. Ong, Wadsworth, and assell&apos; have made a careful kinetic study of sphalerite oxidation under these "normal conditions" and have concluded that the rate of the reaction is controlled by the decomposition of an activated complex adsorbed on the sphalerite surface. They found the rate of oxidation to be small at 700°C. Extrapolation of their data to 400°C would indicate an almost negligible rate at this temperature. In our work sphalerite was reacted with air, mixtures of SO2, O2, and N2, and mixtures of SO3, O2, and N2 in the temperature range 361o to 527OC. Negligible rates of oxidation were found, except for the gas mixtures containing SOs. With this latter gas, the oxidation of finely divided sphalerite was fairly rapid and zinc sulfate was the product. Based on the limited evidence available, the rate of sphalerite oxidation by SO3 is postulated to be controlled by gaseous diffusion through pores or cracks in the zinc-sulfate coating. This evidence for the direct reaction of sphalerite and SO, at low temperature may prove of importance to the understanding of zinc-sulfate formation in the dust-collecting equipment usually associated with zinc roasters. The roaster gas carries off fine dust, much of which may be unreacted sphalerite. The temperature in dust-collecting equipment drops from the roaster temperature (about 800°C) through the range of temperature we studied, to ambient temperature. Such dusts are known to contain far larger amounts of zinc sulfate than the primary calcine. It has been assumed in the past that this sulfate is formed by reaction of ZnO dust with SO3 (or SO, plus 0,) in the partly cooled gases. Our work shows that an alternative possibility exists—the direct reaction of SO3 with ZnS dust. EXPERIMENTAL Reaction rates for sphalerite at 350° to 600°C are relatively small so that it was necessary to use finely divided material with a relatively large surface area in order to obtain measureable amounts of reaction. In the preliminary experiments, pure mineral sphalerite, ground to pass a 325-mesh sieve, and chemically precipitated ZnS (in the form of an impalpable powder) were used. In the quantitative rate experiments the ground mineral sphalerite was processed in an Infrasizer to obtain a product with particle size between 9 and 18 µ. The analysis of this material was 66.7 pct Zn, 0.09 pct Fe, and 32.7 pct S (theoretical sphalerite is 67.1 pct Zn, 32.9 pct S). The sized powder was carefully mixed and divided into l-g samples. The apparatus used for the quantitative rate measurements is shown in Fig. 1. For the preliminary experiments the following change was made: The external catalyst furnace (B, C)* was not used. *Letters refer to Fig._______1 .___- Rather, when catalysis of the SO2 + O2 reaction was desired, the glass beads in basket M were replaced by vanadium-oxide pellets. Procedure—A l-g sample of ZnS was placed on a shallow stainless-steel tray, I, and spread evenly to a depth of about 1mm. The tray was placed in the reaction assembly and the assembly inserted in the cold furnace. The furnace tube was flushed with dry argon and then heated to the desired reaction temperature. The temperature was controlled to ±0.5oC. Gas mixtures (O2 + N2 or O2 + SO2) were prepared from tank gases by means of a mixing device identical to that employed by Darken and Gurry.2 The total flow rate of gas was 205 ml per min to point A of Fig. 1. The accuracy of the individual and

Jan 1, 1960

By D. M. Schuster, E. Scala

The elastic effects occurring in the matrix of a composite reinforced by discontinuous fibers were studied by means of photoelastic techniques. A hirefringent plastic was employed as the matrix material with high-strength a Al2O3 whiskers as the reinforcing fibers. It was found that for whiskers aligned parallel to the tensile load direction: (I) Matrix reinforcement occurred along the length of the whisker to within about 5 diameters of the whisker tip for a length to diameter ratio, L/D, of 40. (2) Significant stress concentrations were created in regions immediately surrounding the tips; the fine as-formed tapered ends exhibited the minimum stress concentration whereas the square-ended whisker produced relatively high values, K r 2.5 for L/D = 40. (3) The axial and radial stress distributions could he determined quantitatively; the stress distribution at the whisker-matrix interface was in general agreement with theoretical calculations. (4) The highest source of stress concentration occurred at points of fracture in whiskers which had ruptured after incorporation into the composite. Whiskers aligned perpendicular to the load direction neither reinforced nor caused appreciahle stress concentrations in the matrix. ThE properties of composites have generally been formulated empirically on the basis of macroscopic tests. There are still many questions concerning the mechanical and chemical interactions occurring at the interface between the reinforcing fiber and its matrix. Continuously reinforced plastics and dispersion-hardened metals represent the two extremes of composite reinforcement. Whether artificially produced or formed in situ, the whisker composite falls between these two extremes and is an example of discontinuous fiber reinforcement. The effect of fiber shape, size, surface condition, and end configuration on the stress distribution in the matrix is important since the presence of stress concentrations, especially in any high-strength, thin-wall structure, could become the cause of catastrophic failure. DOW,&apos; in his theoretical discussion of discontinuous fiber reinforcement, has pointed out that appreciable stress concentrations occur at the tips or ends of the reinforcing fibers. It is the purpose of this study to examine directly, by means of the photoelastic technique, the stresses which occur in the vicinity of a discontinuity or whisker tip and to measure qualitatively and quantitatively the effects of whisker geometry when embedded in a birefringent matrix material. The use of sapphire (a A1,O3) whiskers was decided upon as the reinforcing agent because of their high elastic modulus (E- 60 X 106 psi) and in some cases strengths in excess of one and a half million psi. Sapphire whiskers are of further practical interest since they retain large fractions of their strength up to temperatures approaching the melting point (3720oF).2 The whiskers were grown, by the vapor-phase reaction commonly employed,3 as part of this study to insure a physically uniform supply. Tensile and bend tests were performed to verify that the whiskers were of the expected ultra-high strength. The high-strength whiskers can be identified and selected from the combustion boats by surface perfection, shape, and size; otherwise, strength values can vary by a factor of ten or more. Macroscopic defects are quite common on the surface of large bladed whiskers and the principal experiments were conducted with hexagonal whiskers of about 0.002 in. diameter and lengths ranging from 0.1 to 0.4 in. Upon completion of these two phases of the experiment, several birefringent resins were evaluated. A plastic, developed by Zandman,4 which is supplied by the Budd Co., was found most suitable and was used as the matrix material for the whisker composite throughout the study. It has a sensitivity of 60.5 lb per in. order, calibrated in tension and cures without introducing residual stresses. Young&apos;s modulus for this matrix material is 430,000 psi in the fully cured condition. Since good wetting and bonding between the sapphire and the matrix material is essential to the interpretation of the results, a wettability test was performed. The contact angle was measured to be 168 deg where perfect wetting is defined as 180 deg; therefore, the Budd Plastic wets the sapphire

Jan 1, 1964

By D. H. Baldwin, R. E. Reed-Hill

Six compositions of polycrystalline ZY-0 alloys, containing up to 4.2 at. pct 0, were tested in tension between 77° and 600° K. The data obtained from each of the compositions corresponded closely to a rela-ion between yield stress and absolute temperature of the form In s/so = BT, where oo is the yield stress extrapolated to zero degrees and B is a constant. In agreement with others who have observed this relationship, it is shown that the activation energy may be expressed as Ho In so/s. In the present specimens Ho is approximately 18,000 cal per mole and is apparently independent of temperature and composition inside the limits of the investigation. It is also demonstrated that this form of activation energy cowesponds to a strain rate sensitivity parameter RT/Ho. Oxygen was also noted to have an effect upon the operative deformation mechanisms. With increasing oxygen concentration there was an increased tendency to observe both nonbasal slip and cross-slip phenomena. Oxygen does not seriously inhibit twinning more than it does slip. Twins were observed in all specimens tested. It is becoming increasingly evident that interstitial atoms in solid solution are able to interact strongly with mobile dislocations. Stein, Low, and seybolt,&apos; have shown that, if the carbon concentration in bcc iron is lowered below the solubility limit, its flow stress temperature dependence is markedly reduced. This suggests that carbon atoms in interstitial solid solution may be responsible for the pronounced temperature dependence of the flow stress normally observed in iron. This view has recently been challenged by Leslie and sober2 who observed a strong flow stress temperature dependence in iron to which a trace of titanium had been added in order to remove carbon atoms from solution. Since the interstitial concentration must be reduced below approximately 1 ppm in order to produce a pronounced effect on the flow stress temperature dependence,&apos; studies of the effect of interstitials on the flow stress in iron necessarily involve serious experimental difficulties in alloy preparation. There are other metals, however, in which strong effects of interstitial solutes upon both the flow stress and its temperature dependence are observed. Of particular significance is zirconium which, according to Domagala and Mcpherson, 3 is capable of dissolving 28.6 at. pct O. The O-Zr alloy system is an almost ideal system for studying the interaction of interstitial atoms with deformation modes since it is possible to form alloys capable of study over an extensive range of compositions. Mills has made such a study using single crystals oriented primarily for single prismatic slip4 and has found an effect of oxygen concentration on the flow stress temperature dependence analogous to that observed in iron due to carbon by Stein, Low, and Seybolt. The present paper is specifically concerned with the effect of oxygen on deformation in polycrystalline zirconium. Although plastic flow in this type of specimen is much more complex than that reported for the single-crystal work, and involves both slip (on several different types of planes) and mechanical twinning, the results of this investigation are in general agreement with the single-crystal observations concerning the effect of oxygen on the temperature dependence of the flow stress. In addition, they also demonstrate that oxygen affects the acting deformation systems. This is in contrast to single-crystal results4 that showed only single slip on a prism plane. EXPERIMENTAL PROCEDURE Material. High-purity hot-rolled zirconium strip, 0.2 in. thick by 4 in. wide, of 0.10-mm average grain diameter, was used for forming alloys. It was obtained from the Carborundum Metals Co., Akron, N.Y., whose analysis indicated the major impurities were, in wt ppm: Hf, 540, C, 145; Fe, 100; and 0, <80. The plate texture was similar to a wire texture, with basal planes generally parallel to the rolling direction and basal poles randomly distributed about the rolling direction. The heat treatments described below did not appreciably alter the basic texture. specimen Preparation. Small threaded-end tensile specimens were machined from the plate with axes perpendicular to the rolling direction. These transverse specimens had gage sections 1 in. long by 0.060 in. in diam. The small gage section diameter was dictated by the fact that the alloys were formed by dif-

Jan 1, 1969

By J. A. Coll, R. W. Cahn, A. Lawley

WHILE the creep properties of pure face-centered-cubic and close-packed-hexagonal metals have been thoroughly investigated and are well established, body-centered-cubic metals have been studied less extensively. Moreover, very few fundamental studies on the creep of solid solutions, irrespective of crystal structure, have been reported. The present study is concerned with the creep of a series of body-centered-cubic solid solutions. The present position concerning creep of pure metals is, briefly, as follows.1"3 Creep at first takes place at a steadily decreasing rate; this is the stage termed primary or transient creep. Except at the lowest temperatures this is succeeded by a stage of secondary or steady-state creep. At high temperatures and stresses, this may be succeeded by an accelerating stage, termed tertiary creep, with which we shall not here be concerned. There is no well-defined physical model at present for the transient stage; in general terms, transient creep is best regarded simply as a manifestation of work-harden ing. Steady-stage creep can certainly take place by several different mechanisms: the choice of dominant mechanism depends primarily on temperature. We shall here be concerned only with high-temperature steady-state creep, a term usually reserved for creep at absolute temperatures higher than 0.5 Tm, where T, is the melting point. In this range, the activation energy for creep is, for many metals, equal to the activation energy for self-diffusion, and this is generally interpreted in terms of a "climb mechanism.1-4 The creep rate is determined by the speed at which dislocations, impeded by obstacles the nature of which is disputed but which are probably established during transient creep, can climb by means of a diffusion process, until they are able to by-pass the obstacle. In solid solutions, the intrinsic resistance to the slip motion of dislocations may be much larger than in the solvent, to the extent that the motion of dislocations in the glide plane, rather than their escape by climb out of this plane, may become the rate-controlling factor. weertman5 has considered this possibility from a theoretical point of view, and concluded that some form of "viscous slip" is likely to be rate-controlling at comparatively low stresses. The resistance to slip may arise from "atmospheres" of impurities forming around dislocations; a high Peierls force in materials of high cohesion; or some structural peculiarity such as clustering or ordering of solute atoms.= We shall be concerned here with the case of ordering. The only published investigations concerned explicitly with the effect of order on creep refer to creep in ß-brass by Herman and Brown,7 and in Ni-Fe alloys, by Kornilov and panasyuk8 and by Suzuki and Yamamoto.9 Recently, Herman and Brown&apos;s paper has been supplemented by a determination of the tensile yield point of ß-brass as a function of temperature.10 Both studies showed a sharp drop in resistance to deformation of ß-brass over a range of a few degrees just above the critical temperature Tc at which order finally disappears. These observations are especially noteworthy, because in ß brass the degree of order diminishes steadzly to zero as the temperature approaches Tc. It is, therefore, the disappearance of the last traces of long-range order which has the largest effect on the resistance of the alloy to plastic deformation. In the Ni/Fe alloys of various compositions, resistance to creep at a given temperature and stress is maximum at the stoichiometric composition, both below Tc, (long-range order), and above T,. (short-range order).&apos; Near Tc, the creep resistance of an ordered alloy is much higher than that of the same alloy in the disordered condition.9 The aim of the present investigation was to study the creep behavior in the neighborhood of Tc, of another system of ordering alloys. The iron-aluminum alloys were considered the most suitable. because: i) The order again diminishes steadily to zero as the temperature approaches Tc; there is no sudden drop in order at Tc, and it therefore is

Jan 1, 1961

By F. H. Callaway, W. O. Keller

The various theories as to the well spacing-recovery relationship are reviewed in considerable detail and these theories analyzed in terms of their consistency with modern reservoir engineering concepts. It is concluded that the well spacing problem must be analyzed in terms of recovery efficiency and that a positive answer to the relation between well density and recovery efficiency is not available from direct comparisons of the production histories of wells and fields. The results of an engineering analysis designed to permit approximate calculation of recovery efficiencies as a function of well spacing in a depletion type reservoir from basic reservoir data is presented. Results of this type analysis indicate that the effect of well spacing on recovery efficiency in depletion type reservoirs can be expected to be very small. Limitations of this approach are pointed out, particularly with respect to its application in lenticular reservoirs. Testing techniques are outlined which should indicate whether or not a reservoir is continuous between wells and whether or not satisfactory drainage is being obtained with present spacings. A mass of data of this type indicates continuity to exist in most fields. INTRODUCTION The purpose of this paper is to review critically the engineering aspects of the well spacing problem, both from the standpoint of certain concepts and from the standpoint of reservoir mechanics. The well spacing problem is primarily an economic problem in which the optimum well density for a particular field is that density which will yield the greatest oil recovery consistent with justifiable development costs. The well spacing answer in terms of economic conditions, however, is extremely sensitive to the variation in recovery efficiency with well density. The variation in recovery efficiency with &apos;References given at end of paper. Manuscript received at the office of the Petroleum Branch October 2, 1949. Paper presented at the Petroleum Branch Meeting in San Antonio. Texas, October 5-7. 1949. well density is properly an engineering problem. Different opinions as to the correct answer to this engineering problem is the basis for most of the wide difference in opinion among various members of the industry as to optimum well spacing. This paper will be confined to the engineering problem of the relation between well density and ultimate oil recovery; economic considerations necessary for the evaluation of optimum well density for any particular field will not be discussed. The paper can be logically divided into two parts. The first part deals with a critical examination of the background and logic of the Cutler Rule and of similar studies by other authors and of related well spacing concepts. It is indicated that the variations in recoveries with well density* observed by Cutler and. others can be logically attributed to regional migration. Theoretical justification of the Cutler type relation wherein observed variations in recovery with well density in the same field is attributed to variations in recovery effiiency, in terms of energy relations, is refuted. The second part consists of a review of concepts of reservoir mechanics with regard to the well density-recovery relation. It is indicated that little variation of recovery efficiency with well density can be expected in a depletion type reservoir, unless lenticular conditions prevent communication between wells. The significance of field test data with regard to the existence or non-existence of lenticular conditions is pointed out. THE CUTLER RULE The first published article concerning the engineering aspects of the well spacing problem to receive wide attention was the work of W. W. Cutler&apos; of the U. S. Bureau of Mines, published in 1924. In a study of decline curves from a large *The expression "well density" as utilized herein refers to the number of acres attributed to each well in a uniform well pattern, and is expressed in acres per well. The term "well spacing" Is utilized to denote the average distance between adjacent wells in a uniform well pattern. †Although the Cutler rule is treated critically in this discussion the authors intend no personal criticism of W. W. Cutler or of his hark The currently accepted concepts of reservoir mechanics were no": existent at the time of Cutler&apos;s work, as were even the moat basic tools (such as the bottom hole pressure bomb) for observing reservoir behavior.

Jan 1, 1950

By C. G. Dunn, F. Lionetti

The energy associated with grain boundaries in polycrystalline aggregates is believed to play a major role in grain growth processes and, when growth ceases, to determine the final equilibrium grain boundary angles. Further, the energy of grain boundaries of recrystallization nuclei is a factor in nucleation processes. It is important to know, therefore, how the energy per unit area of a grain boundary, that is, the grain boundary surface tension y, depends on the difference in orientation of the two lattices of the grains producing the boundary. Although the problem is important, surprisingly little has been done toward a quantitative evaluation of the effect of orientation difference on grain boundary energies. C. S. Smith1 recently has discussed this problem and in addition to showing effects of orientation difference on equilibrium angles has shown a variety of interesting effects of surface tension on the appearance of microstructures. Fig 1 and the following relations expressed in Eq 1, which connect equilibrium grain boundary angles and surface tensions, illustrate equilibrium conditions which are believed to hold true in metals. ?l2 _ ?23 _ ?l3 [1] sin ?3 sin ?1 sin ?2 Clearly any two of these surface tensions can be expressed in terms of the third when the equilibrium angles ?1, ?2, and ?3 are known. Applied to the present problem for solid state equilibrium of three grains, the angles ?1,?2 and ?3 must be measured in a plane perpendicular to the line of junction of the three grains. Normally a direct determination of these angles from random microsections is impossible. Consequently Harker and Parker2 and Smith1 (except for some measurements on flat specimens) resorted to a statistical method to determine equilibrium grain boundary angles. Smith reported that grain boundaries meet the surface of a piece of metal nearly perpendicularly. He reported also, in connection with direct angle measurements on flat specimens with grains extending through the thickness, that angles varied appreciably from 120" and concluded that there was a measurable effect of orientation difference on surface tension. Another direct way of determining equilibrium angles and a method adaptable to studying particular configurations, recently suggested by Dunn,³ is to use a three-grain flat specimen with orientations of grains so chosen that the junction line of the three grains will be straight throughout the thickness and perpendicular to the surface of the specimen. Choice of orientations is possible when individual grains of each group can be grown to predetermined orientations through the reorienting and growth of " seed crystals " as described.³ Not only is it possible, for example, to have grains with the same crystallographic plane in the plane of the specimen, but a given orientation difference between two grains can be made a common factor to an unlimited number of three-grain groups while a series of orientation differences is investigated. Any effect of anisotropy of gas-solid surface tension due to grain orientation should be minimized by having all gains oriented the same with regard to crystallographic plane in the plane of the specimen. Another feature of the three-grain group is the notched grain boundaries as shown in Fig 2 for one specimen (S4). The notches serve to anchor the end positions of the grain boundaries (especially at high temperatures) while the central and junction point of the grains moves toward an equilibrium position. Final equilibrium should produce straight grain boundaries if the notches are very narrow and if changes in orientation* of the grain boundary do not alter the surface tension.† If one assumes the straight line condition and no change of surface tension with small changes in grain boundary orientation and finds the equilibrium configuration by a minimization of the grain boundary energy, one obtains the relations given in Eq 1. The approach to straight line boundaries or to minimum energy configurations in specimens containing large grains, such as those used in the present investigation, may be very slow compared with the approach to equilibrium conditions for the grain boundary angles. It may be desirable, as proved to be the case in the present investiga-

Jan 1, 1950

By W. F. Hosford, E. W. Kelley

Deformation studies have been conducted at room temperature on single crystals of magnesium and magnesium alloys with thorium and with lithium. Single crystals oriented to suppress shear on the easily activated basal slip systems were deformed by plane-strain compression. Compression along the C axis was accommodated by {1011} banding. Compression perpendicular to the unconstrained c axis activated {1012} twinning, and, after virtually complete twinning, deformation continued by {1011) banding in the twinned material. Compression perpendicular to the constrained c axis was accommodated by the simultaneous operation of (1012) twinning against the constraint and (1011 ) banding. Although this orientation was favorable for {1010)(1210) prism and {1011}(1~10) pyramidal slip, these modes were not observed in pure magnesium or in Mg-0.5 pct Th. However, {10i0)(1~10) prism slip was observed in crystals of Mg-4 pct Li during compression perpendicular to the constrained c axis. Fracture in all materials occurred parallel to (1124) or {l~il) depending on the orientation and composition of the specimen. THE mechanical behavior of the hcp metals is strongly anisotropic. Although several slip systems have been reported the slip is cpmmonly in the directions of closest packing, the (1210),&apos; and this does not produce strains parallel to the c axis. Hence the inherent anisotropy. The deformation mode most easily activated in magnesium at room temperature is (0001)(1210)- basal slip. Also {1010}(1~10) prism slip and {1011)(1210) pyramidal slip have been reported, primarily at elevated temperatures.2"4 However, at room temperature the shear stresses to activate the prism and pyramidal modes are roughly a hundredfold greater than that required for basal slip.&apos;j4 Thus prism and pyramidal slip may be expected only under special conditions of loading. Strains normal to the basal plane can be produced by twinning, however. Many twinning modes have been reported for magnesium,&apos; with (1012) twinning the most common and relatively easy to activate. Magnesium can deform by (1012) twinning when stressed along the c axis jn tension, but not in compression. In contrast, (1011) twinning is activated by compression along the c axis and not by tension. In addition to primary twinning, secondary twinning or slip can occur within the reoriented material of primary twins.&apos; In general at least five independent shear systems must be active to bring about an arbitrary shape change such as that in the individual grains of a deforming polycrystalline material.&apos; Because basal slip can_ provide only two independent shear systems and (1012) twinning can only accommodate an extension of the c axis, other deformation modes must be active in magnesium for an arbitrary shape change to occur. The purpose of this investigation has therefore been to study the various deformation modes in magnesium at room temperature, with special emphasis on those modes that are less easily activated. The effect of the alloying elements, thorium and lithium, has also been investigated. In polycrystalline aggregates, unambiguous identification of deformation modes is extremely difficult and the direct evaluation of the resolved shear stresses to activate them is not feasible. On the other hand, uni-axial tension and compression experiments on single crystals may not activate some of the- deformation modes because basal slip and/or {1012) twinning cannot be suppressed in most orientations. However, it should be possible to activate all possible deformation modes using oriented single crystals and plane-strain compression. Identification of active deformation systems and evaluation of the resolved shear stresses required to activate them should be facilitated. Wonsiewicz and Backofen have recently completed an investigation of the plasticity of pure magnesium crystals at various temperatures utilizing plane-strain compression and selected crystal orientations. This technique has also been used in the present work. The seven orientations selected for study are indicated in Table I. Plane-strain compression along the c axis (orientations A and B) should activate some deformation mode _other than basal, prism, or pyramidal slip, or (1012) twinning. In orientations C and D, prism or pyramidal slip would be expected to take place. When the compressive load is applied perpendicular to an unconstrained c axis (orientations E and F) the three slip modes should be suppressed but not (10i2) twinning. In orientation G, basal slip should occur.

Jan 1, 1969

By Nicholas J. Grant, A. W. Mullendore

Measurements of grain boundary sliding were made on polycrystal and bicrystal tensile creep specimens of Al-2 pct Mg at 500oand 700oF. Grain and pain boundary orientation factors were studied with respect to their effect on the magnitude and direction of grain boundary sliding. It was concluded that a large part of the observed sliding may be caused by the operation of slip crossing the grain boundaries. Supporting evidence for this model from other investigations is also given. GRAIN boundary sliding in metals during elevated temperature deformation has frequently been thought of as an independent mechanism with its own characteristic stress, temperature, and structure dependence. Further, it is common to regard the grain boundary as the weak link during creep deformation since: 1) the strength of apolycrystallinemetal, as meas-sured by creep rate or rupture life, decreases at\a more rapid rate when sliding comes into action, and 2) grain boundary sliding, as revealed by "boundary darkening" and fold formation is often the first visible deformation. On the other hand, more quantitative observations, in both polycrystals and bicrystals, have shown boundary deformation to be closely related to the over-all deformation of the specimen. The curve of grain boundary contribution to elongation vs time takes a shape similar to that of the total creep curve,&apos;,&apos; and the apparent activation energy for sliding appears in most cases to have the same value as that for total creep.3 In order to reconcile these observations, one is left with these possibilities: 1) The grain boundary and grain deformation rates are both controlled by the same rate limiting processes. 2) The rate of sliding is limited by accommodation deformation in the grains. 3) Sliding is the consequence of grain deformation. 4) Grain deformation is dependent on prior grain boundary deformation. Alternatives 2) and 3) would view grain boundary sliding as occurring in series with another deformation process which could be rate controlling. McLean prefers item 3) as the sliding basis,4 where subgrain rotation results from dislocation accumulation in the substructure at the grain boundary. Crussard and Friedel&apos;s5 treatment of grain boundary migration considers that dislocations are forced into the grain boundary and are dissociated into dislocations with Burgers&apos; vectors nearly parallel to the grain boundary. The movement of these partial grain boundary dislocations then produces the sliding. The results of this investigation have indicated alternative 3) to be the most appropriate and it is this aspect of grain boundary sliding which will be analyzed. EXPERIMENTAL PROCEDURE Three types of tensile creep tests were employed in this study: (I) A constant load test of one very coarsegrained polycrystalline specimen at 500° F, 3600 psi, 1 pct per/hr strain rate to examine the grain and grain boundary orientation factors in grain boundary sliding. (II) Constant strain rate tests of polycrystalline specimens at 510o and 715o F, 2 pct per/hr strain rate to determine the grain boundary contribution to elongation at very low total strains. (m) Constant strain rate tests of bicrystals of various grain and grain boundary orientations at 500°F, 2 pct per/hr strain rate to obtain further information on the orientation effects in grain boundary sliding. The material used in the tests was a high-purity Al-1&apos;.92 mg alloy, kindly furnished by Alcoa. Its composition is given in Table I. The alloy is a solid solution at the test temperatures. The coarse grained polycrystalline specimen for test (I) was prepared by recrystallizingthe machined specimen, straining it about 1pct intension at room temperature and annealing at 900°F for 8hr. The constant strain rate specimens (11), with an 178 in. sq. by 1/2 in. long gage section, were cut from 1/8 in. thick sheet of cold rolled and annealed (8 hr at 1000oF) material. The latter specimens were supported in a special jig during the milling operations to avoid any bending, and the gage section was subsequently heavily electropolished to remove the cold-worked surface layer. The bicrystals (ID) were machined in the same

Jan 1, 1963